Problem: Solve for $x$ and $y$ using substitution. ${2x-2y = 4}$ ${y = -2x+7}$
Solution: Since $y$ has already been solved for, substitute $-2x+7$ for $y$ in the first equation. ${2x - 2}{(-2x+7)}{= 4}$ Simplify and solve for $x$ $2x+4x - 14 = 4$ $6x-14 = 4$ $6x-14{+14} = 4{+14}$ $6x = 18$ $\dfrac{6x}{{6}} = \dfrac{18}{{6}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {y = -2x+7}\thinspace$ to find $y$ ${y = -2}{(3)}{ + 7}$ $y = -6 + 7$ $y = 1$ You can also plug ${x = 3}$ into $\thinspace {2x-2y = 4}\thinspace$ and get the same answer for $y$ : ${2}{(3)}{ - 2y = 4}$ ${y = 1}$